Subgroups — C₁₃×#34489 #15720828

Order 3328.

2032 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2344	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#2313	C₂	1	2	yes	maximal, complemented
21	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
24	C₁₃×#554	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	2	yes	—
43	C₁₃×#391	C₂²	1	2	yes	—
44	C₁₃×#391	C₂²	1	2	yes	—
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#390	C₂²	1	1	yes	characteristic
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#389	C₂²	1	1	yes	characteristic
56	C₁₃×#389	C₂²	1	1	yes	characteristic
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	1	yes	characteristic
74	C₁₃×#387	C₂²	1	1	yes	characteristic
75	C₁₃×#387	C₂²	1	1	yes	characteristic
76	C₁₃×#387	C₂²	1	1	yes	characteristic
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#387	C₂²	1	2	yes	—
88	C₁₃×#387	C₂²	1	2	yes	—
89	C₁₃×#387	C₂²	1	2	yes	—
90	C₁₃×#387	C₂²	1	2	yes	—
91	C₁₃×#384	C₂²	1	1	yes	characteristic
92	C₁₃×#382	C₂²	1	1	yes	characteristic
93	C₁₃×#382	C₂²	1	1	yes	characteristic
94	C₁₃×#381	C₂²	1	2	yes	—
95	C₁₃×#381	C₂²	1	2	yes	—
96	C₁₃×#381	C₂²	1	2	yes	—
97	C₁₃×#381	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	—
100	C₁₃×#380	C₂²	1	2	yes	—
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₁₃×#376	C₂²	1	1	yes	characteristic
122	C₁₃×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
131	C₁₃×#125	C₂×C₄	1	8	yes	—
132	C₁₃×#125	C₂×C₄	1	8	yes	—
133	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
134	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
135	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
136	C₄×Q₈×C₁₃	—	4	4	no	—
137	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
138	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
139	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
140	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
141	C₁₃×#117	—	4	4	no	—
142	C₁₃×#117	—	4	4	no	—
143	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	1	yes	characteristic
205	C₁₃×#95	C₂³	1	1	yes	characteristic
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	1	yes	characteristic
211	C₁₃×#95	C₂³	1	1	yes	characteristic
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
216	C₁₃×#95	C₂³	1	1	yes	characteristic
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	1	yes	characteristic
231	C₁₃×#95	C₂³	1	1	yes	characteristic
232	C₁₃×#95	C₂³	1	1	yes	characteristic
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	1	yes	characteristic
236	C₁₃×#95	C₂³	1	1	yes	characteristic
237	#34489	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₃	—	4	2	no	—
240	C₂×Q₈×C₁₃	—	4	1	no	—
241	C₂×Q₈×C₁₃	—	4	1	no	—
242	C₂×Q₈×C₁₃	—	4	2	no	—
243	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
244	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	—	4	2	no	—
250	C₂²×C₄×C₁₃	—	4	2	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	—	4	2	no	—
253	C₂²×C₄×C₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
255	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
256	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	4	2	no	—
287	C₁₃×C₄⋊C₄	—	4	2	no	—
288	C₁₃×C₄⋊C₄	—	4	1	no	—
289	C₁₃×C₄⋊C₄	—	4	1	no	—
290	C₁₃×C₄⋊C₄	—	4	2	no	—
291	C₁₃×C₄⋊C₄	—	4	1	no	—
292	C₁₃×C₄⋊C₄	—	4	2	no	—
293	C₁₃×C₄⋊C₄	—	4	1	no	—
294	C₁₃×C₄⋊C₄	—	4	2	no	—
295	C₁₃×C₄⋊C₄	—	4	2	no	—
296	C₁₃×C₄⋊C₄	—	4	2	no	—
297	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
298	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
299	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
300	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
301	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
302	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
306	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	4	2	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
317	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
318	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	4	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	4	2	no	—
326	C₄²×C₁₃	—	4	1	no	—
327	C₄²×C₁₃	—	4	2	no	—
328	C₄²×C₁₃	—	4	2	no	—
329	C₄²×C₁₃	—	4	1	no	—
330	C₄²×C₁₃	—	4	1	no	—
331	C₄²×C₁₃	—	4	2	no	—
332	C₄²×C₁₃	—	4	2	no	—
333	C₄²×C₁₃	—	4	2	no	—
334	C₄²×C₁₃	—	4	2	no	—
335	C₄²×C₁₃	—	4	2	no	—
336	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
337	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
338	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
339	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
340	#2378	C₂×C₁₃	1	2	yes	complemented
341	#2378	C₂×C₁₃	1	2	yes	complemented
342	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#2362	C₂×C₁₃	1	2	yes	complemented
346	#2357	C₂×C₁₃	1	1	yes	characteristic
347	#2357	C₂×C₁₃	1	1	yes	characteristic
348	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2354	C₂×C₁₃	1	1	yes	characteristic
350	#2344	C₂×C₁₃	1	2	yes	complemented
351	#2332	C₂×C₁₃	1	2	yes	complemented
352	#2332	C₂×C₁₃	1	2	yes	complemented
353	#2331	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2330	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#2323	C₂×C₁₃	1	2	yes	complemented
356	#2319	C₂×C₁₃	1	1	yes	characteristic
357	#2319	C₂×C₁₃	1	1	yes	characteristic
358	#2313	C₂×C₁₃	1	2	yes	complemented
359	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#2293	C₂×C₁₃	1	1	yes	characteristic
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
369	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
370	Q₈×C₁₃	—	4	4	no	—
371	Q₈×C₁₃	—	4	8	no	—
372	D₄×C₁₃	—	2	8	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	4	8	no	—
427	C₂×C₄×C₁₃	—	4	8	no	—
428	C₂×C₄×C₁₃	—	4	8	no	—
429	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
433	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
436	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
437	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
438	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
441	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
442	#554	C₄×C₁₃	1	16	yes	complemented
443	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
447	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
448	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
449	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
450	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#117	C₂²×C₁₃	1	2	yes	—
455	C₂×#117	C₂²×C₁₃	1	2	yes	—
456	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
457	#391	C₂²×C₁₃	1	2	yes	—
458	#391	C₂²×C₁₃	1	2	yes	—
459	#391	C₂²×C₁₃	1	1	yes	characteristic
460	#391	C₂²×C₁₃	1	2	yes	—
461	#391	C₂²×C₁₃	1	2	yes	—
462	#391	C₂²×C₁₃	1	1	yes	characteristic
463	#390	C₂²×C₁₃	1	1	yes	characteristic
464	#390	C₂²×C₁₃	1	1	yes	characteristic
465	#390	C₂²×C₁₃	1	1	yes	characteristic
466	#390	C₂²×C₁₃	1	1	yes	characteristic
467	#389	C₂²×C₁₃	1	1	yes	characteristic
468	#389	C₂²×C₁₃	1	1	yes	characteristic
469	#389	C₂²×C₁₃	1	1	yes	characteristic
470	#389	C₂²×C₁₃	1	1	yes	characteristic
471	#389	C₂²×C₁₃	1	1	yes	characteristic
472	#389	C₂²×C₁₃	1	2	yes	—
473	#389	C₂²×C₁₃	1	2	yes	—
474	#389	C₂²×C₁₃	1	1	yes	characteristic
475	#389	C₂²×C₁₃	1	2	yes	—
476	#389	C₂²×C₁₃	1	2	yes	—
477	#389	C₂²×C₁₃	1	1	yes	characteristic
478	#389	C₂²×C₁₃	1	1	yes	characteristic
479	#388	C₂²×C₁₃	1	2	yes	—
480	#388	C₂²×C₁₃	1	2	yes	—
481	#388	C₂²×C₁₃	1	2	yes	—
482	#388	C₂²×C₁₃	1	2	yes	—
483	#388	C₂²×C₁₃	1	2	yes	—
484	#388	C₂²×C₁₃	1	2	yes	—
485	#388	C₂²×C₁₃	1	2	yes	—
486	#388	C₂²×C₁₃	1	2	yes	—
487	#388	C₂²×C₁₃	1	2	yes	—
488	#388	C₂²×C₁₃	1	2	yes	—
489	#388	C₂²×C₁₃	1	2	yes	—
490	#388	C₂²×C₁₃	1	2	yes	—
491	#387	C₂²×C₁₃	1	2	yes	—
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	1	yes	characteristic
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#387	C₂²×C₁₃	1	2	yes	—
498	#387	C₂²×C₁₃	1	2	yes	—
499	#387	C₂²×C₁₃	1	2	yes	—
500	#387	C₂²×C₁₃	1	2	yes	—
501	#387	C₂²×C₁₃	1	2	yes	—
502	#387	C₂²×C₁₃	1	2	yes	—
503	#387	C₂²×C₁₃	1	1	yes	characteristic
504	#387	C₂²×C₁₃	1	2	yes	—
505	#387	C₂²×C₁₃	1	2	yes	—
506	#387	C₂²×C₁₃	1	2	yes	—
507	#387	C₂²×C₁₃	1	1	yes	characteristic
508	#387	C₂²×C₁₃	1	1	yes	characteristic
509	#384	C₂²×C₁₃	1	1	yes	characteristic
510	#382	C₂²×C₁₃	1	1	yes	characteristic
511	#382	C₂²×C₁₃	1	1	yes	characteristic
512	#381	C₂²×C₁₃	1	2	yes	—
513	#381	C₂²×C₁₃	1	2	yes	—
514	#381	C₂²×C₁₃	1	2	yes	—
515	#381	C₂²×C₁₃	1	2	yes	—
516	#380	C₂²×C₁₃	1	2	yes	—
517	#380	C₂²×C₁₃	1	2	yes	—
518	#380	C₂²×C₁₃	1	2	yes	—
519	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
531	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
532	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
539	#376	C₂²×C₁₃	1	1	yes	characteristic
540	#376	C₂²×C₁₃	1	1	yes	characteristic
541	C₄³	C₂²×C₁₃	1	1	yes	characteristic
542	C₂²×C₁₃	—	2	4	no	—
543	C₂²×C₁₃	—	2	4	no	—
544	C₂²×C₁₃	—	2	4	no	—
545	C₂²×C₁₃	—	4	2	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	—	4	2	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
550	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₂²×C₁₃	#585	1	1	yes	characteristic
554	C₂²×C₁₃	#585	1	1	yes	characteristic
555	C₂²×C₁₃	#585	1	1	yes	characteristic
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	2	4	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	4	no	—
563	C₄×C₁₃	—	2	4	no	—
564	C₄×C₁₃	—	2	2	no	—
565	C₄×C₁₃	—	2	2	no	—
566	C₄×C₁₃	—	4	2	no	—
567	C₄×C₁₃	—	4	1	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	1	no	—
570	C₄×C₁₃	—	4	2	no	—
571	C₄×C₁₃	—	4	1	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	—	4	1	no	—
575	C₄×C₁₃	—	4	1	no	—
576	C₄×C₁₃	—	4	1	no	—
577	C₄×C₁₃	#519	1	4	yes	—
578	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
579	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
582	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
584	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
585	#125	C₂×C₄×C₁₃	1	8	yes	—
586	#125	C₂×C₄×C₁₃	1	8	yes	—
587	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
588	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
589	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
590	C₄×Q₈	—	4	4	no	—
591	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
592	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
593	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
594	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
595	#117	—	4	4	no	—
596	#117	—	4	4	no	—
597	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	#95	C₂³×C₁₃	1	1	yes	characteristic
659	#95	C₂³×C₁₃	1	1	yes	characteristic
660	#95	C₂³×C₁₃	1	1	yes	characteristic
661	#95	C₂³×C₁₃	1	1	yes	characteristic
662	#95	C₂³×C₁₃	1	1	yes	characteristic
663	#95	C₂³×C₁₃	1	1	yes	characteristic
664	#95	C₂³×C₁₃	1	1	yes	characteristic
665	#95	C₂³×C₁₃	1	1	yes	characteristic
666	#95	C₂³×C₁₃	1	1	yes	characteristic
667	#95	C₂³×C₁₃	1	1	yes	characteristic
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	1	yes	characteristic
673	#95	C₂³×C₁₃	1	1	yes	characteristic
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	1	yes	characteristic
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	2	yes	—
681	#95	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	2	yes	—
683	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	#95	C₂³×C₁₃	1	2	yes	—
689	#95	C₂³×C₁₃	1	1	yes	characteristic
690	#95	C₂³×C₁₃	1	2	yes	—
691	C₂×C₁₃	—	4	4	no	—
692	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
693	C₂×C₁₃	#3428	1	1	yes	characteristic
694	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂×C₁₃	#3554	1	1	yes	characteristic
696	C₂×C₁₃	#3557	1	1	yes	characteristic
697	C₂×C₁₃	#3559	1	1	yes	characteristic
698	C₂×C₁₃	#3565	1	1	yes	characteristic
699	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	—	4	1	no	—
702	C₂×Q₈	—	4	1	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
705	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
716	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
717	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	1	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	1	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
759	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
760	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
761	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
762	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
763	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
764	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
765	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
766	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
767	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
768	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
778	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
779	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	4	2	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	1	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	1	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	2	no	—
797	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
798	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
799	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
800	C₁₃	#34489	1	1	yes	characteristic, direct product factor, Sylow
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
808	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
809	Q₈	—	4	4	no	—
810	Q₈	—	4	8	no	—
811	D₄	—	2	8	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
869	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
870	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
872	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
873	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
874	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
875	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
876	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
877	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
878	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
879	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
880	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
889	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
891	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
892	C₂²	C₁₃×#585	1	1	yes	characteristic
893	C₂²	C₁₃×#585	1	1	yes	characteristic
894	C₂²	C₁₃×#585	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	4	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	1	no	—
916	C₄	C₁₃×#519	1	4	yes	—
917	C₂	—	4	4	no	—
918	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
919	C₂	C₁₃×#3428	1	1	yes	characteristic
920	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
921	C₂	C₁₃×#3554	1	1	yes	characteristic
922	C₂	C₁₃×#3557	1	1	yes	characteristic
923	C₂	C₁₃×#3559	1	1	yes	characteristic
924	C₂	C₁₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#2378	C₂	semidirect
3. C₁₃×#2378	C₂	semidirect
4. C₁₃×#2370	C₂	semidirect
5. C₁₃×#2370	C₂	semidirect
6. C₁₃×#2365	C₂	semidirect
7. C₁₃×#2362	C₂	semidirect
10. C₁₃×#2355	C₂	semidirect
12. C₁₃×#2344	C₂	semidirect
13. C₁₃×#2332	C₂	semidirect
14. C₁₃×#2332	C₂	semidirect
15. C₁₃×#2331	C₂	semidirect
16. C₁₃×#2330	C₂	semidirect
17. C₁₃×#2323	C₂	semidirect
20. C₁₃×#2313	C₂	semidirect
21. C₄×C₁₃×#125	C₂	semidirect
22. C₁₃×#2295	C₂	semidirect
24. C₁₃×#554	C₄	semidirect
237. #34489	C₁₃	direct (N × H)
340. #2378	C₂×C₁₃	semidirect
341. #2378	C₂×C₁₃	semidirect
342. #2370	C₂×C₁₃	semidirect
343. #2370	C₂×C₁₃	semidirect
344. #2365	C₂×C₁₃	semidirect
345. #2362	C₂×C₁₃	semidirect
348. #2355	C₂×C₁₃	semidirect
350. #2344	C₂×C₁₃	semidirect
351. #2332	C₂×C₁₃	semidirect
352. #2332	C₂×C₁₃	semidirect
353. #2331	C₂×C₁₃	semidirect
354. #2330	C₂×C₁₃	semidirect
355. #2323	C₂×C₁₃	semidirect
358. #2313	C₂×C₁₃	semidirect
359. C₄×#125	C₂×C₁₃	semidirect
360. #2295	C₂×C₁₃	semidirect
442. #554	C₄×C₁₃	semidirect
800. C₁₃	#34489	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#554	2
C₁₃×#2378	2
C₁₃×#2370	2
C₁₃×#2365	2
C₁₃×#2362	2
C₁₃×#2357	2
C₁₃×#2355	2
C₁₃×#2354	2
C₁₃×#2344	2
C₁₃×#2332	2
C₁₃×#2331	2
C₁₃×#2330	2
C₁₃×#2323	2
C₁₃×#2319	2
C₁₃×#2313	2
C₄×C₁₃×#125	2
C₁₃×#2295	2
C₁₃×#2293	2
#34489	13

Subgroups — C13×#34489 #15720828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34489 #15720828